A352797 Let S(k) be the subsequence of multiples of k from k*positive integers where each element of S(k) sets a new record of divisors in that sequence. Then f(k) is the first element from S(k)/k that is not a power of 2. Sequence lists records for f(k).

1, 3, 9, 45, 135, 945, 2835, 14175, 155925, 467775, 6081075

Offset

1,2

Comments

Conjecture: Subsequence of A147516.

Links

Table of n, a(n) for n=1..11.

Example

For k=1, the sequence of multiples of 1 that set records for numbers of divisors (divided by 1) starts 1,2,4,6. (A002182)
For k=3, the sequence starts 1,2,4,8,12. (A351623)
For k=9, the sequence starts 1,2,4,8,16,20.
For k=45, the sequence starts 1,2,4,8,16,24.

Prog

(PARI) isp2(n) = if (n<=2, return(1)); my(m); ispower(n, , &m) && (m==2);
f(n) = {my(m=1, nm, k=1, ok=0); until(ok, nm = numdiv(k*n); if (nm > m, m = nm; if (!isp2(k), ok = 1); ); if (!ok, k++); ); k; }
lista(nn) = {my(m=1, fm); for (n=1, nn, fm = f(n); if (fm > m, m = fm; print1(n, ", "); ); ); } \\ Michel Marcus, May 05 2022

Crossrefs

Cf. A002182, A351623, A147516.

Sequence in context: A209977 A001902 A224085 * A192891 A364296 A068100

Adjacent sequences: A352794 A352795 A352796 * A352798 A352799 A352800

Keyword

nonn,more

Author

J. Lowell, Apr 03 2022

Status

approved